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Decay estimates for the wave and Dirac equations with a magnetic potential

✍ Scribed by Piero D'Ancona; Luca Fanelli

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
260 KB
Volume
60
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

We study the electromagnetic wave equation and the perturbed massless Dirac equation on ℝ~t~ Γ— ℝ^3^:

where the potentials A(x), B(x), and V(x) are assumed to be small but may be rough. For both equations, we prove the expected time decay rate of the solution

where the norm β€–fβ€–~X~ can be expressed as the weighted L^2^‐norm of a few derivatives of the data f. Β© 2006 Wiley Periodicals, Inc.

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